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Simplifying 4x + x2 + -175 = 0 Reorder the terms: -175 + 4x + x2 = 0 Solving -175 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '175' to each side of the equation. -175 + 4x + 175 + x2 = 0 + 175 Reorder the terms: -175 + 175 + 4x + x2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + 4x + x2 = 0 + 175 4x + x2 = 0 + 175 Combine like terms: 0 + 175 = 175 4x + x2 = 175 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 175 + 4 Reorder the terms: 4 + 4x + x2 = 175 + 4 Combine like terms: 175 + 4 = 179 4 + 4x + x2 = 179 Factor a perfect square on the left side: (x + 2)(x + 2) = 179 Calculate the square root of the right side: 13.37908816 Break this problem into two subproblems by setting (x + 2) equal to 13.37908816 and -13.37908816.Subproblem 1
x + 2 = 13.37908816 Simplifying x + 2 = 13.37908816 Reorder the terms: 2 + x = 13.37908816 Solving 2 + x = 13.37908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 13.37908816 + -2 Combine like terms: 2 + -2 = 0 0 + x = 13.37908816 + -2 x = 13.37908816 + -2 Combine like terms: 13.37908816 + -2 = 11.37908816 x = 11.37908816 Simplifying x = 11.37908816Subproblem 2
x + 2 = -13.37908816 Simplifying x + 2 = -13.37908816 Reorder the terms: 2 + x = -13.37908816 Solving 2 + x = -13.37908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -13.37908816 + -2 Combine like terms: 2 + -2 = 0 0 + x = -13.37908816 + -2 x = -13.37908816 + -2 Combine like terms: -13.37908816 + -2 = -15.37908816 x = -15.37908816 Simplifying x = -15.37908816Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.37908816, -15.37908816}
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